Every relationship is made much more efficient if you just start apologizing on day one and keep apologizing for everything. If the other person says "You apologize too much!", apologize for that, too. Eventually, they’ll write you a very big check to go away and stop bothering them._________________Hiromichi

I think this is someone who is not really serious, and it looks to me like the person who wrote it meant exactly what it said. The idea is if you apologize for everything and apologize so much that the other person can't stand it anymore, they will write you a big check to just go away and stop bothering them. It doesn't really make sense because why would you want to apologize so much and who would write a check to make you go away? But I guess the writer wanted to make that point.